Preview pose mode when making change to armature in edit mode
Unfortunately there is no way to view the same object in two different modes at the same time. I've never really had a problem with how blender handles this though, as tabbing between modes is quite quick. If you have to adjust your viewport every time you switch modes you could try having two viewports open with two different angles. Being able to view an animation while also being able to edit the skeleton would definitely be handy though.